The second definition of conic curve is easier to understand in polar coordinate system.

An ellipse is a conic curve. If you pay attention, ellipse, hyperbola and parabola are all discussed in the same chapter of the textbook. Generally speaking, conic curves include these three kinds. In fact, there are other situations, namely, a point, a circle, two intersecting straight lines and a straight line.

For the second definition of conic curve, the most important part is the proportional constant e, which distinguishes the shape of trajectory according to the range of e.

Namely: 0

E= 1 is a parabola.

E> 1 is a hyperbola.

In the polar coordinate system, the expressions of the above three curves are the same, but the difference is e.

Polar coordinate expression:

ρ=ep/( 1-ecosθ)

P is the distance from the moving point to the alignment, and e is the eccentricity. By limiting the range of e, the above three curves can be obtained respectively.